A question about nonabelian finite simple groups

Question

Let $G$ be a nonabelian finite simple group of lie type on finite field $F$ and $s\in G$ be a semisimpl element of $G$, $i.e.$ an element with order coprime to $Char(F)$. Also suppose $T$ is a maximal torus of $G$ containing $s$. Is it true that $T\subseteq C_G(s)$ where $C_G(s)=\{g\in G:~sg=gs\}$?

Answer 1

Any torus, in particular any maximal torus is by definition an abelian subgroup. So the answer is yes, and the assumption about $s$ being semisimple is not needed.